Download a. Solve b. Find the x-intercepts of a. What are the solutions

1. a. Solve 8x  xx  4  0
b. Find the x-intercepts of f x   8x  xx  4
a. What are the solutions?
(Simplify your answer. Type exact answers, using radicals as needed. Express complex numbers
in terms of i. Use a comma to separate answers as needed.)
b. What are the x-intercepts?
(Type an ordered pair. Simplify your answer. Type an exact answer, using radicals as needed.
Express complex numbers in terms of i. Use a comma to separate answers as needed.)
2. Determine the nature of the solutions of the equation
3. Find and label the vertex and the line of symmetry. Graph the function
1
f x    x 2
3
The vertex is
(Type and ordered pair.)
The equation of the line of symmetry is x =
Graph f x 
4. The width of a rectangle is 3 ft less than the length. The area is 4 ft 2 . Find the length and the
width.
5. For the scatterplot, determine which of the following types of functions might be used as a
model for the data
6. Find and label the vertex and the line of symmetry. Graph the function
f  x   2 x  1
2
The vertex is
(Type an ordered pair.)
The equation of the line of symmetry is x =
Graph the function.
7. A student opens a mathematics book to two factoring pages. The product of the page number is
1980. Find the page numbers
The first page is
The second page is
8. Find the vertex, the line of symmetry, the maximum or minimum value of the quadratic
function, and then graph the function.
f x   x 2  10 x  4
What is the vertex?
(Type an ordered pair.)
What is the equation of the line of symmetry?
X=
What is the max/min of f(x)?
Is the value, f 5  29 a minimum or a maximum?
Graph f(x)
9. Solve by completing the square.
m2 
9
3
m
2
2
The solutions are
(Use radicals as needed. Use a comma to separate answers.)
10. Determine the nature of the solutions of the equation
x 2  11  0
Choose the nature of the solutions of the equation.
a. 1 real solution
b. 2 imaginary solutions
c. 2 real solutions
11. Find the vertex, the line of symmetry, the maximum or minimum value of the quadratic
function, and then graph the function.
f x   5  x 2
What is the vertex?
(Type an ordered pair.)
What is the equation of the line of symmetry?
X=
What is the max/min of f(x)?
Is the value, f 0  5 a minimum or a maximum
Graph f(x)
12. Find the vertex, the line of symmetry, and the max or min value of f(x). Graph the function
f x   4x  5  1
2
The vertex is?
(Type an ordered pair.)
The line of symmetry is x =
The max/min value of f(x) is
Is the value, f  5  1a min or a max
Graph f(x)
13. Give exact and approximate solutions to three decimal places.
x 2  3x  5  0
The exact solutions are
(Use radicals as needed. Use a comma to separate answers.)
The approximate solutions to 3 decimal places are
(Use a comma to separate answers.)
14. Find the x-intercepts and y-intercepts.
f x    x 2  4 x  45
The c-coordinates of the intercepts are x =
(Use a comma to separate answers. Type N if there are no intercepts.)
The y-intercept is (0,?)
(Type N if there are no intercepts.)
15. Write a quadratic equation having the given numbers as solutions.
-11 and -9
The quadratic equation is ? = 0
(Type the answer in standard form. Type an expression using x as a variable.)
16. The number of tickets sold each day for an upcoming performance of Handel’s Messiah is given
by N x   0.4 x 2  9.6 x  10 , where x is the number of days since the concert was first
announced. When will daily ticket sales peak and how many tickets will be sold that day?
Ticket sales will peak ? days after the concert was first announced.
The number of tickets sold on that day will be?
(Round to the nearest integer.)
17. Give exact and approximate solutions to three decimal places.
x 2  8 x  16  49
What are the exact solutions? X =
(Type an exact answer, using radicals as needed. Rationalize all denominators. Express complex
numbers in the term of i. Use a comma to separate answers as needed.)
18. Solve 4 x 2  20
Find the x-intercepts of f x   4 x 2  20
What are the solutions? X =
(Type an exact answer, using radicals as needed. Rationalize all denominators. Express complex
numbers in the term of i. Use a comma to separate answers as needed.)
What are the x-intercepts?
(Type an ordered pair. Type an exact answer, using radicals as needed. Rationalize all
denominators. Express complex numbers in terms of i. Use a comma to separate answers as
needed. Type N if there are no x-intercepts.)
19. Find the vertex, the line of symmetry, the max/min value of the quadratic function, and graph
the function.
f x   2 x 2  8 x  4
What is the vertex?
(Type an ordered pair.)
What is the equation of the line of symmetry?
X=
What is the max/min of f(x)
Is the value, f x   4 a minimum or a maximum.
Graph f(x)
20. Solve for x
x2  x  2  0
The solution is x =
(Simplify the answer. Type exact answers, using radicals as needed. Type the answer in the form
a + bi. Use a comma to separate answers. Type N if there are no solutions.)
21. Find the vertex, the line of symmetry, and the max/min value of f(x). Graph the function.
f x    x  3  5
2
The vertex is
(Type an ordered pair.)
The line of symmetry is x =
The max/min value of f(x) is?
The value, f  3  5 , is
Minimum or Maximum
Graph the solution.
22. Give exact and approximate solutions to three decimal places.
 x  5 2
 16
What are the exact solutions?
X=
(Type an exact answer, using radicals as needed. Rationalize all denominators. Express complex
numbers in terms of i. Use a comma to separate answers as needed.)
23. Solve the formula for the given letter. Assume all variables represent non-negative numbers.
E  mc 2 , for c